Ranger -
Most engineering majors require several levels of calculus covering derivatives, integrals and matrices. In addition, certain majors require differential equations. Usually that is as far as you go. If one is set on the sciences, most of the core classes required for engineering will serve you in any of the fields. I don't think there would be a huge wast of time if you decided to switch after the first couple of semesters. The first year usually includes your basic physics, chemistry, maybe an introductory engineering class or two, and calculus.
I was actually horrible at math. Ok, not completely relevant, but I struggled with long division back in grammar school. Later, in college, it became easier once I got into the right thought mode. If you are understanding and passing trig, I think you have the analytical thinking necessary to move you to higher levels of math. As long as you are not taking two or three math classes at the same time (I did that, don't do it) it comes slow enough to absorb, so long as you have that analytical thinking capability. If you have to work harder than others, you can still manage so long as you attend EVERY class, take excellent notes, and go to the prof immediately if you get stuck. That should keep you up with everyone else. By the way, even though I struggled with math earlier, I finished with a masters in ME and, if I remember right, only one class shy of a BS in math. (I didn't have the desire to take the necessary abstract math class for the actual BS) It can be done.
Now whether or not you will enjoy all of this is an entirely different matter. You really have to like a challenge. At any rate, part of being an engineer is enjoying a challenge. We are, after all, problem solvers.
Karenlau-
If you are still undecided about the two majors, I would suggest that you speak with a counselor, advisor, someone in the department. Ask what the requirements are for entry into grad school and see if you are already on that path. If you are, perhaps that makes your decision much easier. If not, you must see if there is anything you can do to improve your chances.
To be honest, if you are aiming towards a research position, there are not so many jobs in engineering where you will have that chance. Engineering is applied physics and research is limited to testing methods to solve a particular problem rather than developing completely new concepts. There are a few situations where engineers do, but I think your average job doesn't provide that opportunity.
And wow, I don't think that you should be worried quite yet about your brain power at 28! It is more likely that if you are feeling a bit dull edged, it has to do with stress or particular issues going on in your life at this time. Trust me on this one. I think you will find that once you have resolved any issues, you will be back to your sharp thinking in no time.
